The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to ${2048}^3$ mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, $E^{+}(k_{\perp })$ and $E^{-}(k_{\perp })$, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent $-3/2$ as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with $E^{+}>E^{-}$, the simulations show that $E^{-}\propto k_{\perp }^{-3/2}$ for all Reynolds numbers considered, while $E^{+}$ has a slightly steeper spectrum at small Re. As the Reynolds number increases, $E^{+}$ flattens. Since $E^{\pm }$ are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as $E^{+}\propto E^{-}\propto k_{\perp }^{-3/2}$. Questions regarding the universality of the spectrum and the value of the “Kolmogorov constant” are discussed.

A number of theoretical calculations have studied the effect of radiation-reaction forces on radiation distributions in strong-field counterpropagating electron-beam–laser interactions, but could these effects—including quantum corrections—be observed in interactions with realistic bunches and focusing fields, as is hoped in a number of soon-to-be-proposed experiments? We present numerical calculations of the angularly resolved radiation spectrum from an electron bunch with parameters similar to those produced in laser-wakefield-acceleration experiments, interacting with an intense, ultrashort laser pulse. For our parameters, the effect of radiation damping on the angular distribution and energy distribution of photons is not easily discernible for a realistic moderate-emittance electron beam. However, experiments using such a counterpropagating beam–laser geometry should be able to measure these effects using current laser systems through measurement of the electron-beam properties. In addition, the brilliance of this source is very high, with peak spectral brilliance exceeding ${10}^{29}\mathrm{photons}{\mathrm{s}}^{-1}{\mathrm{mm}}^{-2}{\mathrm{mrad}}^{-2}(0.1\%\mathrm{\text{bandwidth}}{)}^{-1}$ with an approximately 2% conversion efficiency and with a peak energy of 10 MeV.

Many quantum systems are being investigated in the hope of building a large-scale quantum computer. All of these systems suffer from decoherence, resulting in errors during the execution of quantum gates. Quantum error correction enables reliable quantum computation given unreliable hardware. Unoptimized topological quantum error correction (TQEC), while still effective, performs very suboptimally, especially at low error rates. Hand optimizing the classical processing associated with a TQEC scheme for a specific system to achieve better error tolerance can be extremely laborious. We describe a tool, Autotune, capable of performing this optimization automatically, and give two highly distinct examples of its use and extreme outperformance of unoptimized TQEC. Autotune is designed to facilitate the precise study of real hardware running TQEC, with every quantum gate having a realistic, physics-based error model.

We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of $\nu =1/m$, while electrons of the opposite spin occupy a similar state with $\nu =-1/m$. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension $\sqrt{2m}$. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length $\xi$. We show that, for the divergence-free portion of the superfluid velocity field, the kinetic-energy spectrum over wave number $k$ may be decomposed into an ultraviolet regime ($k\gg {\xi }^{-1}$) having a universal $k^{-3}$ scaling arising from the vortex core structure, and an infrared regime ($k\ll {\xi }^{-1}$) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent $-1/3$ for vortices of the same sign of circulation leads to an infrared kinetic-energy spectrum with a Kolmogorov $k^{-5/3}$ power law, which is consistent with the existence of an inertial range. The presence of these $k^{-3}$ and $k^{-5/3}$ power laws, together with the constraint of continuity at the smallest configurational scale $k\approx {\xi }^{-1}$, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous, compressible, two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic-energy distribution, once we introduce the concept of a clustered fraction consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.

Laser-plasma accelerators are prominent candidates for driving next-generation compact light sources, promising high-brightness, few-femtosecond x-ray pulses intrinsically synchronized to an optical laser, and thus are ideally suited for pump-probe experiments with femtosecond resolution. So far, the large spectral width of laser-plasma-driven beams has been preventing a successful free-electron laser (FEL) demonstration using such sources. In this paper, we study the application of an optimized undulator design and bunch decompression to large-energy-spread beams in order to permit FEL amplification. Numerically, we show a proof-of-principle scenario to demonstrate FEL gain in the vacuum ultraviolet range with electron beams from laser-plasma accelerators as currently available in experiments.

Dictionaries link a given word to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that definitions loop back upon themselves. We demonstrate that such definitional loops are created in order to introduce new concepts into a language. In contrast to the expectations for a random lexical network, in graphs of the dictionary, meaningful loops are quite short, although they are often linked to form larger, strongly connected components. These components are found to represent distinct semantic ideas. This observation can be quantified by a singular value decomposition, which uncovers a set of conceptual relationships arising in the global structure of the dictionary. Finally, we use etymological data to show that elements of loops tend to be added to the English lexicon simultaneously and incorporate our results into a simple model for language evolution that falls within the “rich-get-richer” class of network growth.

An effective approach to separating shaped particles is needed to isolate disease-causing cells for diagnostics or to aid in purifying nonspherical particles in applications ranging from food science to drug delivery. However, the separation of shaped particles is generally challenging, since nonspherical particles can freely rotate and present different faces while being sorted. We experimentally and numerically show that inertial fluid-dynamic effects allow for shape-dependent separation of flowing particles. (Spheres and rods with aspect ratios of $3:1$ and $5:1$ have all been separable.) Particle rotation around a conserved axis following Jeffery orbits is found to be a necessary component in producing different equilibrium positions across the channel that depend on particle rotational diameter. These differences are large enough to enable passive, continuous, high-purity, high-throughput, and shape-based separation downstream. Furthermore, we show that this shape-based separation can be applied to a large range of particle sizes and types, including small, artificially made $3\mathrm{\text{−}}\mu \mathrm{m}$ particles as well as bioparticles such as yeast. This practical approach for sorting particles by a previously inaccessible geometric parameter opens up a new capability that should find use in a range of fields.

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement backaction often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that, by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement backaction of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, backaction evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical-force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broadband squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic-spin ensembles, and implementations of the quantum Toffoli gate.

Waves, of wavelength $\lambda$, transmit poorly through apertures of dimensions $\ell \ll \lambda$. Here it is shown that coupling of a subwavelength aperture to an electromagnetic oscillator makes it possible for a focused, diffraction-limited beam that impinges on the aperture to undergo perfect transmission. Ignoring nonradiative losses, and for apertures with closed boundaries in a metallic screen, the transmitted power at the oscillator’s natural frequency is enhanced by a factor of $(\lambda /\ell {)}^6$ compared with the nonresonant case. As a nontrivial extension to apertures with open boundaries, an analytically solvable problem is introduced and analyzed, which involves a pair of arbitrarily small slits in a two-dimensional waveguide. The system displays perfect transmission at a frequency corresponding to that of a quasilocalized, cavitylike mode bound to the slits, the frequency of which is below that of the cutoff mode of the continuum. In contrast, and remarkably, the Fabry-Pérot-like resonance with the extended cutoff mode leads to imperfect transmission, comparable to that of an individual, nonresonated slit. An explanation of this single-slit-like behavior is presented, which also applies to the closely related phenomenon of light funneling concerning transmission through subwavelength channels [see F. Pardo et al., Light Funneling Mechanism Explained by Magnetoelectric Interference, Phys. Rev. Lett. 107, 093902 (2011), and references therein].

The study of human interactions is of central importance for understanding the behavior of individuals, groups, and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links, and we analyze quantitatively the tendencies used to create ties in these evolving online affiliation networks. We show that an accurate estimation of these probabilistic tendencies can be achieved only by following the time evolution of the network. Inferences about the reason for the existence of links using statistical analysis of network snapshots must therefore be made with great caution. Here, we start by characterizing every single link when the tie was established in the network. This information allows us to describe the probabilistic tendencies of tie formation and extract meaningful sociological conclusions. We also find significant differences in behavioral traits in the social tendencies among individuals according to their degree of activity, gender, age, popularity, and other attributes. For instance, in the particular data sets analyzed here, we find that women reciprocate connections 3 times as much as men and that this difference increases with age. Men tend to connect with the most popular people more often than women do, across all ages. On the other hand, triangular tie tendencies are similar, independent of gender, and show an increase with age. These results require further validation in other social settings. Our findings can be useful to build models of realistic social network structures and to discover the underlying laws that govern establishment of ties in evolving social networks.

An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number $N$, which can be mapped to an $N$-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.

Stochastic resonance (SR) is a well-known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic (random or probabilistic) noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively transitions from folded to unfolded configurations under the action of an oscillating mechanical force applied with optical tweezers. By varying the frequency of the force oscillation, we investigate the folding and unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measure several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that a good quantifier of the SR is the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance-matching condition. Finally, we carry out experiments on short hairpins that show how SR might be useful for enhancing the detection of conformational molecular transitions of low SNR.

We present experiments measuring an interaction-induced phase shift of Rydberg atoms at Stark-tuned Förster resonances. The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently. We use a pair-state interferometer to measure the phase shift. Although the coupling between pair states is coherent on the time scale of the experiment, a loss of visibility occurs as a pair-state interferometer involves three simultaneously interfering paths and only one of them is phase shifted by the mutual interaction. Despite additional dephasing mechanisms, a pulsed Förster coupling sequence allows for observation of coherent dynamics around the Förster resonance.

Electromagnetic fields with strong optical chirality can be formed in the near field of chiral plasmonic nanostructures. We calculate and visualize the degree of chirality to identify regions with relatively high values. This analysis leads to design principles for a simple utilization of chiral fields. We investigate planar geometries, which offer a convenient way to access the designated fields, as well as three-dimensional nanostructures, which show a very high local optical chirality.

Complex networks are a highly useful tool for modeling a vast number of different real world structures. Percolation describes the transition to extensive connectedness upon the gradual addition of links. Whether single links may explosively change macroscopic connectivity in networks where, according to certain rules, links are added competitively has been debated intensely in the past three years. In a recent article [O. Riordan and L. Warnke, Explosive Percolation is Continuous, Science 333, 322 (2011).], O. Riordan and L. Warnke conclude that (i) any rule based on picking a fixed number of random vertices gives a continuous transition, and (ii) that explosive percolation is continuous. In contrast, we show that it is equally true that certain percolation processes based on picking a fixed number of random vertices are discontinuous, and we resolve this apparent paradox. We identify and analyze a process that is continuous in the sense defined by Riordan and Warnke but still exhibits infinitely many discontinuous jumps in an arbitrary vicinity of the transition point: a Devil’s staircase. We demonstrate analytically that continuity at the first connectivity transition and discontinuity of the percolation process are compatible for certain competitive percolation systems.

We propose general topological order parameters for interacting insulators in terms of the Green’s function at zero frequency. They provide a unified description of various interacting topological insulators including the quantum anomalous Hall insulators and the time-reversal-invariant insulators in four, three, and two dimensions. Since only the Green’s function at zero frequency is used, these topological order parameters can be evaluated efficiently by most numerical and analytical algorithms for strongly interacting systems.

We develop a layered quantum-computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface-code quantum error correction. In doing so, we propose a new quantum-computer architecture based on optical control of quantum dots. The time scales of physical-hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum-dot architecture we study could solve such problems on the time scale of days.